Correct me if I’m wrong but do you think the lines between the tiles are cement and not grout? That would be highly unlikely and doesn’t appear to be the case from the two photos. The way that tile is installed is usually a two step process. Step one is to adhere the tiles to the surface using thinset or mortar. This leaves all the edges of the tiles exposed as the bottom is the only part stuck down. In step two, all the gaps between the tiles are filled with a colored cement - sometimes with sand, sometimes with polymers, glitter, or other chemicals. This is what dries and what you are wanting to clean. It looks like concrete because it is concrete on a finer scale.

There are many tools on the market to remove grout, just be careful if you go that route not to chip the tile. Regrouting will give you the best results. Otherwise, I make a paste of baking soda and hydrogen peroxide and scrub with a grout brush after letting it sit for 10 minutes. That seems to work for me pretty well.

Having the floor retiled or retiling it yourself are also not very expensive options, and it’s a project that is very satisfying to complete and makes a big change.

Good luck!